Parameterize Mesh or object imported from blender file?
This is what Library Overrides are for :
Create your base object, add a custom property. Don't forget to check Is Library Overridable in the property settings. Use a driver to drive, for instance the scale of your object.

Save your blend file. Go into your work file, and link the cube object. (File &gt; Link &gt; Yourfile.blend &gt; Object &gt; Yourobject)
Select your object, then go to Object &gt; Relations &gt; Make Library Override &gt; Accept the dialog.
This will create another instance of your base object, which is in fact an override. (Piercing arrow and chain icon)

Select the library override, and go to the object properties. Notice your custom prop is not greyed out anymore. You can tweak it as you wish. If you Duplicate your object, you will be able to specify different overrides for this property as well as others. An override property will by default be in a light blue color.

If you want to override the object's material, set the mode to to Object and then you can change it as you wish :